1 Oklahoma State University Spears School of Business Time Value of Money
2 Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. $15,000 cash upon signing the contract 2. $15,000 cash at the end of first year of employment 3. $20,000 cash at the end of the first of employment Cash in hand seems to be no brainer, but! How would be determine whether (3) is better or worse than (1)?
3 Slide 3 The One-Period Case If you were to invest $10,000 at 5-percent interest for one year, your investment would grow to $10,500. $500 would be interest ($10,000.05) $10,000 is the principal repayment ($10,000 1) $10,500 is the total due. It can be calculated as: $10,500 $10,000 (1.05) The total amount due at the end of the investment is call the Future Value(FV FV).
4 Slide 4 Future Value In the one-period case, the formula for FVcan be written as: FV C 0 (1 + r) Where C 0 is cash flow today (time zero), and r is the appropriate interest rate.
5 Slide 5 Present Value If you were to be promised $10,000 due in one year when interest rates are 5-percent, your investment would be worth $9, in today s dollars. $ 9, The amount that a borrower would need to set aside today to be able to meet the promised payment of $10,000 in one year is called the Present Value(PV PV). Note that $10,000 $9, (1.05). $10,
6 Slide 6 Present Value In the one-period case, the formula for PVcan be written as: PV C r Where C1 is cash flow at date 1, and r is the appropriate interest rate.
7 Slide 7 Net Present Value The Net Present Value (NPV) of an investment is the present value of the expected cash flows, less the cost of the investment. Suppose an investment that promises to pay $10,000 in one year is offered for sale for $9,500. Your interest rate is 5%. Should you buy?
8 Slide 8 Net Present Value PV PV $10,000 $9, $9,500+ $9, PV $23.81 The present value of the cash inflow is greater than the cost. In other words, the Net Present Value is positive, so the investment should be purchased.
9 Slide 9 Net Present Value In the one-period case, the formula for NPVcan be written as: NPV Cost+ PV If we had notundertaken the positive NPVproject considered on the last slide, and instead invested our $9,500 elsewhere at 5 percent, our FVwould be less than the $10,000 the investment promised, and we would be worse off in FVterms : $9,500 (1.05) $9,975 < $10,000
10 Slide 10 The Multiperiod Case The general formula for the future value of an investment over many periods can be written as: FV C 0 (1 + r) T Where C 0 is cash flow at date zero, r is the appropriate interest rate, and Tis the number of periods over which the cash is invested.
11 Slide 11 The Multiperiod Case, Cont d The general formula for the present value of an investment over many periods can be written as: PV Where C T is cash flow at date T, C 1 T ( r) T r is the appropriate interest rate, and Tis the number of periods over which the cash is invested.
12 Slide 12 Future Value Suppose a stock currently pays a dividend of $1.10, which is expected to grow at 40% per year for the next five years. What will the dividend be in five years? FV C 0 (1 + r) T $5.92 $1.10 (1.40) 5
13 Slide 13 Future Value and Compounding Notice that the dividend in year five, $5.92, is considerably higher than the sum of the original dividend plus five increases of 40-percent on the original $1.10 dividend: $5.92 > $ [$ ] $3.30 This is due to compounding.
15 Slide 15 Present Value and Discounting How much would an investor have to set aside today in order to have $20,000 five years from now if the current rate is 15%? PV $20, $ 9, $20,000 5 (1.15)
16 Slide 16 How Long is the Wait? If we deposit $5,000 today in an account paying 10%, how long does it take to grow to $10,000? FV C (1 r) 0 + T T $10,000 ( 1.10) $5,000 T ln( 1.10) $ 10,000 $5,000 ln(2) 2 T (1.10) T ln(2) ln(1.10) years
17 Slide 17 What Rate Is Enough? Assume the total cost of a college education will be $50,000 when your child enters college in 12 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your child s education? T 12 C0 (1+ r $ 50,000 $5,000 (1+ r) FV ) About 21.15%. (1+ r) 12 $50,000 $5, ( 1+ r) r
18 Slide 18 Calculator Keys Texas Instruments BA-II Plus FV future value PV present value I/Y periodic interest rate P/Y must equal 1 for the I/Y to be the periodic rate Interest is entered as a percent, not a decimal N number of periods Remember to clear the registers (CLR TVM) after each problem Other calculators are similar in format
19 Slide 19 Multiple Cash Flows Consider an investment that pays $200 one year from now, with cash flows increasing by $200 per year through year 4. If the interest rate is 12%, what is the present value of this stream of cash flows? If the issuer offers this investment for $1,500, should you purchase it?
20 Slide 20 Multiple Cash Flows , Present Value < Cost Do Not Purchase
21 Slide 21 Valuing Lumpy Cash Flows First, set your calculator to 1 payment per year. Then, use the cash flow menu: CF0 0 CF3 600 I 12 CF1 200 F3 1 NPV F1 1 CF , CF2 400 F4 1 F2 1
22 Slide 22 Compounding Periods Compounding an investment mtimes a year for T years provides for future value of wealth: FV C 1+ 0 r m m T
23 Slide 23 Compounding Periods For example, if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to 2.12 FV $ $50 (1.06) 6 $70.93
24 Slide 24 Effective Annual Rates of Interest A reasonable question to ask in the above example is what is the effective annualrate of interest on that investment? FV $50 (1+ ) $50 (1.06) $ The Effective Annual Rate (EAR) of interest is the annual rate that would give us the same end-ofinvestment wealth after 3 years: $50 (1+ EAR) 3 $70.93
25 Slide 25 Effective Annual Rates of Interest FV $50 (1+ EAR) 3 $70.93 EAR (1+ EAR) $70.93 $ $70.93 $ So, investing at 12.36% compounded annually is the same as investing at 12% compounded semi-annually. 3
26 Slide 26 Effective Annual Rates of Interest Find the Effective Annual Rate (EAR) of an 18% APR loan that is compounded monthly. What we have is a loan with a monthly interest rate rate of 1½%. This is equivalent to a loan with an annual interest rate of 19.56%. n m r 1 + m (1.015)
27 Slide 27 EAR on a Financial Calculator Texas Instruments BAII Plus keys: description: [2nd] [ICONV] Opens interest rate conversion menu [ ] [C/Y] 12 [ENTER] Sets 12 payments per year [ ][NOM] 18 [ENTER] Sets 18 APR. [ ] [EFF] [CPT] 19.56
28 Slide 28 Continuous Compounding The general formula for the future value of an investment compounded continuously over many periods can be written as: FV C 0 e rt Where C 0 is cash flow at date 0, r is the stated annual interest rate, Tis the number of years, and eis a transcendental number approximately equal to e x is a key on your calculator.
29 Slide 29 Classical Cash Flow Schemes Perpetuity A constant stream of cash flows that lasts forever Growing perpetuity A stream of cash flows that grows at a constant rate forever Annuity A stream of constant cash flows that lasts for a fixed number of periods Growing annuity A stream of cash flows that grows at a constant rate for a fixed number of periods
30 Slide 30 Perpetuity A constant stream of cash flows that lasts forever C C C PV PV C C C ( 1+ r) (1+ r) (1+ r) 3 C r +L
31 Slide 31 Perpetuity: Example What is the value of a British consol that promises to pay 15 every year for ever? The interest rate is 10-percent PV
32 Slide 32 Growing Perpetuity A growing stream of cash flows that lasts forever C C (1+g) C (1+g) 2 0 PV PV C C (1+ g) C (1+ g) ( 1+ r) (1+ r) (1+ r) 3 C r g 2 +L
33 Slide 33 Growing Perpetuity: Example The expected dividend next year is $1.30, and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream? $1.30 $1.30 (1.05) $1.30 (1.05) PV $ $26.00
34 Slide 34 Annuity A constant stream of cash flows with a fixed maturity C C C C L T PV C C C L 2 3 (1+ r) (1+ r) (1+ r) (1 C + r ) T PV C r 1 1 (1+ r) T
35 Slide 35 Annuity: Example If you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36-month loans? $400 $400 $400 L $ PV $ / ( ) 36 $12,954.59
36 Slide 36 What is the present value of a four-year annuity of $100 per year that makes its first payment two years from today if the discount rate is 9%? PV $100 (1.09) $100 (1.09) $100 (1.09) $100 (1.09) $100 (1.09) t t 1 $ $ $ $100 $100 $100 $ $ PV $
37 Slide 37 Growing Annuity A growing stream of cash flows with a fixed maturity C 0 1 PV PV C (1+ r) r C g + 1 C (1+ g) 2 (1+ r) C (1+g) 2 1+ (1+ g r ) T + L+ C (1+g) 2 3 L C (1+ g) T (1+ r) C (1+g) T-1 T T 1
38 Slide 38 Growing Annuity: Example A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3% each year. What is the present value at retirement if the discount rate is 10%? $20, PV $20, $20,000 (1.03) $20,000 (1.03) 39 L 40 $265,121.57
39 Slide 39 Growing Annuity: Example You are evaluating an income generating property. Net rent is received at the end of each year. The first year's rent is expected to be $8,500, and rent is expected to increase 7% each year. What is the present value of the estimated income stream over the first 5 years if the discount rate is 12%? 3 $8,500 (1.07) 2 $8,500 (1.07) $8,500 (1.07) $8,500 $8,500 $ 9,095 $9, $10, (1.07) $11, $34,706.26
40 Slide 40 What Is a Firm Worth? Conceptually, a firm should be worth the present value of the firm s cash flows. The tricky part is determining the size, timing, and risk of those cash flows.
1.-1.3 ime Value of Money and Discounted ash Flows ime Value of Money (VM) - the Intuition A cash flow today is worth more than a cash flow in the future since: Individuals prefer present consumption to
McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit $100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,
Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.
BUSI Financial Management Time Value of Money 1 Time Value of Money (TVM) Present value and future value how much is $1 now worth in the future? how much is $1 in the future worth now? Business planning
Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has built-in preset assumptions
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
Solutions Manual Corporate Finance Ross, Westerfield, and Jaffe 9 th edition 1 CHAPTER 1 INTRODUCTION TO CORPORATE FINANCE Answers to Concept Questions 1. In the corporate form of ownership, the shareholders
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 4 work problems. Questions in the multiple choice section will be either concept or calculation
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
Chapter Discounted Cash Flow Valuation Compounding Periods Other Than Annual Let s examine monthly compounding problems. Future Value Suppose you invest $9,000 today and get an interest rate of 9 percent
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator
QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost
Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
International Financial Strategies 1 Future Value and Compounding Future value = cash value of the investment at some point in the future Investing for single period: FV. Future Value PV. Present Value
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
Texas Instruments Graphing Calculators have a built in app that may be used to compute quantities involved in compound interest, annuities, and amortization. For the examples below, we ll utilize the screens
Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted
CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3
The Time Value of Money Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original
How to Calculate Present Values Michael Frantz, 2010-09-22 Present Value What is the Present Value The Present Value is the value today of tomorrow s cash flows. It is based on the fact that a Euro tomorrow
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11 th Global Edition McGraw-Hill Education Copyright 2014 by The McGraw-Hill Companies, Inc. All rights
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
HANDBOOK: HOW TO USE YOUR TI BA II PLUS CALCULATOR This document is designed to provide you with (1) the basics of how your TI BA II Plus financial calculator operates, and (2) the typical keystrokes that
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students
Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values
Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
Chartered Financial Analyst Program Texas Instruments BA II Plus calculator tutorial Nicholas J Blain, CFA Chief Executive Quartic Training 1 outline 0. Calculator setup and introduction 1. Basic algebra
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde" -- to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
Review Solutions 1. Planning to use the money to finish your last year in school, you deposit $4,000 into a savings account with a quoted annual interest rate (APR) of 8% and quarterly compounding. Fifteen
1. You are trying to estimate the required rate of return for a particular investment. Which of the following premiums are you least likely to consider? A. Inflation premium B. Maturity premium C. Nominal
Using the Finance Menu of the TI-83/84/Plus calculators KEY To get to the FINANCE menu On the TI-83 press 2 nd x -1 On the TI-83, TI-83 Plus, TI-84, or TI-84 Plus press APPS and then select 1:FINANCE The
This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
D-How to Use a Financial Calculator* Most personal finance decisions involve calculations of the time value of money. Three methods are used to compute this value: time value of money tables (such as those
Your consent to our cookies if you continue to use this website.